In this talk, I will present some of our recent work on low rank methods for time-dependent differential equations. In the first part, we focus on the Lindblad master equation arising from modeling of open quantum systems. A defining feature of the Lindblad equation is the completely positivity and trace preserving (CPTP) property of the solution. We present a high order accurate low rank method with CPTP property. In the second part, we focus on stiff matrix differential equation, and present a new preconditioner based on dynamic low rank approximation for the low rank GMRES scheme. This is joint work with Shixu Meng (VT) and Daniel Appelo (VT).